The function \(\psi \)  essentially corresponds to a node-attribute transformation, which depends on the distributions \(\mathbb {P}_{\pm 1}\) . As these distributions are unknown in practice, a NN model to learn \(\psi \)  is suggested, such as the one in the model APPNP [1]} and GPR-GNN [2]}. Due to the expressivity of NNs [3]}, [4]}, a wide range of \(\psi \)  can be modeled. One insightful example is that when \(\mathbb {P}_{\pm 1}\)  are Laplace distributions, \(\psi \)  is a bounded function (same as \(\phi \) ) to control the heavy-tailed attributes generated by Laplace distributions.
